Semi-implicit finite difference method for non-hydrostatic, free-surface flows

摘要

In this paper a semi-implicit finite difference model for non-hydrostatic, free-surface flows is analyzed and discussed. It is shown that the present algorithm is generally more accurate than recently developed models for quasi-hydrostatic flows. The governing equations are the free-surface Navier-Stokes equations defined on a general, irregular domain of arbitrary scale. The momentum equations, the incompressibility condition and the equation for the free-surface are integrated by a semi-implicit algorithm in such a fashion that the resulting numerical solution is mass conservative and unconditionally stable with respect to the gravity wave speed, wind stress, vertical viscosity and bottom friction.